If in a hyperbola, the distance between the foci is 10 and transverse axis has length 8, then the length of its latus rectum is

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Aicharya · Accepted Answer

Given, $ 2 a e=10 	ext { and } 2 a=8 $ $ a e=5, a=4 $ In hyperbola, $ \begin{aligned} & & (a e)^2 & =a^2+b^2 \ \Rightarrow & & 25 & =16+b^2 \ \Rightarrow & & b^2 & =9 \end{aligned} $ Length of latus rectum $=\frac{2 b^2}{a}=\frac{2 	imes 9}{4}=\frac{9}{2}$

If in a hyperbola, the distance between the foci is 10 and transverse axis has length 8, then the length of…

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